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    <title>sylm</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>sylm</b> -  Sylvester matrix</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[S]=sylm(a,b)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>a,b</b>
        </tt>: two polynomials</li>
      <li>
        <tt>
          <b>S</b>
        </tt>: matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>sylm(a,b)</b>
      </tt> gives the Sylvester matrix associated to polynomials
    <tt>
        <b>a</b>
      </tt> and <tt>
        <b>b</b>
      </tt>, i.e. the matrix <tt>
        <b>S</b>
      </tt> such that:</p>
    <p>
      <tt>
        <b>coeff( a*x + b*y )' = S * [coeff(x)';coeff(y)']</b>
      </tt>.</p>
    <p>
    Dimension of <tt>
        <b>S</b>
      </tt> is equal to <tt>
        <b>degree(a)+degree(b)</b>
      </tt>.</p>
    <p>
    If <tt>
        <b>a</b>
      </tt> and <tt>
        <b>b</b>
      </tt> are coprime polynomials then</p>
    <p>
      <tt>
        <b>rank(sylm(a,b))=degree(a)+degree(b))</b>
      </tt> and the instructions</p>
    <pre>

  u = sylm(a,b) \ eye(na+nb,1)
  x = poly(u(1:nb),'z','coeff')
  y = poly(u(nb+1:na+nb),'z','coeff')
   
    </pre>
    <p>
    compute Bezout factors <tt>
        <b>x</b>
      </tt> and <tt>
        <b>y</b>
      </tt> of minimal degree 
    such that <tt>
        <b>a*x+b*y = 1</b>
      </tt>
    </p>
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